Definition of Differentiation

Sarah Miller

5 min read

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Study Guide Overview

This study guide covers instantaneous rate of change, focusing on its definition as the slope of a graph at a specific point. It explains how to calculate it using limits and its relationship to the derivative. Examples, practice questions, and a glossary of key terms (including average rate of change) are provided.

#Instantaneous Rate of Change

#Table of Contents

What is the Instantaneous Rate of Change?
Finding the Instantaneous Rate of Change
Worked Example
Practice Questions
Glossary
Summary and Key Takeaways

#What is the Instantaneous Rate of Change?

The instantaneous rate of change is the slope of a graph at a specific point, rather than between two points.

Key Concept

The instantaneous rate of change at a point on a function is essentially the derivative at that point. It measures how the function value changes as the input changes infinitesimally.

#Finding the Instantaneous Rate of Change

Consider the graph of a function $f$ with two points on the graph, $A$ and $B$ :

#Average Rate of Change

Using the labeling on the left:

The average rate of change from $A$ to $B$ can be written as: $\frac{f(x) - f(a)}{x - a}$

Using the labeling on the right:

T...

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